For a complete understanding of the physical processes causing the photometric variability of pre-main sequence systems, simultaneous optical and near-IR observations are required to disentangle the emission from the stars and that from their associated circumstellar disks. Data of this sort are extremely rare and little systematic work has been reported to date. The work presented in this paper is a systematic attempt in this direction. It presents an analysis of the simultaneous optical and near-IR photometric variability of 18 Herbig Ae/Be and T Tauri stars which were observed in October 98 by the EXPORT collaboration. The time difference between the UBVRI and JHK measurements is less than 1 hour in ~50% of the data and the largest difference is around 2 hours in only ~10% of the data. Twelve stars appear to show a correlation between the optical and near-IR variability trends, which suggests a common physical origin such as spots and/or variable extinction. The optical and near-IR variability is uncorrelated in the rest of the objects, which suggests it originates in distinctly different regions. In general, the optical variability qualitatively follows the predictions of starspots or variable extinction. As far as the near-IR is concerned, the simultaneity of the observations demonstrates that for most objects the flux is largely produced by their circumstellar disks and, consequently, in many cases the near-IR fluctuations must be attributed to structural variations of such disks producing variations of their thermal emission and/or scattered light. The observed near-IR changes of up to around 1 mag on timescales of 1-2 days provide interesting challenges for understanding the mechanisms generating such remarkable variabilities, an issue insufficiently investigated until now but one which deserves further theoretical and modeling efforts.